Changeset 166

Timestamp:

08/24/15 16:34:01 (9 years ago)

Author:

leila_ocean

Message:

added real exp cnrs tests

Location:

altifloat/doc/ocean_modelling

Files:

• Draft1.tex (added)
• elsarticle-template-harv.tex (modified) (2 diffs)
• fig/tf144_win24_mov6_dive4_coef4.fig (added)
• fig/tf144_win24_mov6_dive7_coef10.fig (added)

altifloat/doc/ocean_modelling/elsarticle-template-harv.tex

@@ -39 +39 @@
 %% The amssymb package provides various useful mathematical symbols
 \usepackage{amssymb}
+\usepackage{multimedia}
+\usepackage{amsfonts}
+\usepackage{amsmath}
+\usepackage{multimedia}
+\usepackage{graphics}
+\usepackage{bbm}
+\usepackage{pstricks}
+\usepackage{amsthm}
+ \usepackage{graphics}
+ \usepackage{pgf}
+ \usepackage{wrapfig} 
+ \usepackage{mathtools} 
+ \newcommand{\vectornorm}[1]{\left|\left|#1\right|\right|}
+ \newcommand{\bo}[1]{\mathbf{#1}}
+%\newcommand{\vectornorm}[1]{\left|\left|#1\right|\right|}
+\newcommand{\dif}[2]{\frac{\partial #1}{\partial #2}}
+\newcommand{\diff}[2]{\frac{\partial^2 #1}{\partial {#2}^2}}
+\newcommand{\odif}[2]{\frac{d #1}{d #2}} 
+\newcommand{\odiff}[2]{\frac{d^2 #1}{d #2^2}}
+
 %% The amsthm package provides extended theorem environments
 %% \usepackage{amsthm}
@@ -108 +128 @@
 \section{Data}
 \section{Method}
+\begin{itemize} 
+
+\item $\vec{U_0}=\vec{U}_{b}+\vec{\delta U},$ $\vec{U}_b=\textcolor{red}{\vec{U}_{alt}}$ and $\vec{r}=\vec{r}^{\,b}+\vec{\delta r}$
+\item Model and Linear tangent (forward Euler for the numerical integration, and bilinear Lagrange interpolation in space for instance):  
+\small{
+\begin{align} \notag
+&\vec{r}^{\,b}_i(k\delta t)=\vec{r}^{\,b}_i((k-1)\delta t)+2\delta t \, interp(\vec{U}^b, \vec{r}^{\,b}_i((k-1)\delta t)),\,\,\,\,\, \text{\textcolor{blue}{model}}  \\  \notag
+&\vec{\delta r}_i(k\delta t) = \vec{\delta r}_i((k-1)\delta t) + 2 \delta t \, \{ interp(\textcolor{green}{\vec{\delta U}},\vec{r}^{\,b}_i((k-1)\delta t)) \\ \notag 
+&+ \vec{\delta {r}}_i((k-1)\delta t) \cdot \partial _{(x,y)} interp (\vec{U}^b,\vec{r}^{\,b}_i((k-1)\delta t))\}  \,\,\, \text{\textcolor{blue}{tangent}} \notag
+\end{align}
+initialized with observations, for $k=1,2,3, \cdots $ and $i=1, \cdots N_{drift}$ 
+}
+%\vec{r}(0)= \vec{r}^{o}(0)$
+\item Perform sequences of optimization
+\[\mathcal{J}(\textcolor{green}{\delta \vec{U}})= \frac{1}{2} \left \{ \sum _i \sum_{m=1}^{P} \vectornorm{\vec{r}^{\,b}_i+\delta \vec{r}_i(\textcolor{green}{\delta \vec{U}}) -\vec{r}_i^{\,o}(m\Delta t) }^2 +\vectornorm{ \textcolor{green}{\vec{\delta U}} }^2_{\bo{B}}  \right\}   \]
+$P$ depends on $T_{L}/\Delta t$. $T_L$ characteristic of autocorrelation of drifters (typical 1-3 days) 
+
+%+\sum_{i,m=1}^{m=P} \vectornorm{\vec{r}^{\,b}+\delta \vec{r}(\textcolor{green}{\delta \vec{u}}) -\vec{r}_i^{\,o}(m\Delta t) }^2   \right]   \]
+\end{itemize}
+
+
+
+
 \section{Twin Experiments}
 \section{Experiment with Real Data}